Final answer:
The relationship that must be true if polygon ABCD rotates 70° counterclockwise about point E to give polygon A'B'C'D' is BB′ = DD′. When a polygon rotates counterclockwise, the corresponding sides remain equal in length.
Step-by-step explanation:
The relationship that must be true if polygon ABCD rotates 70° counterclockwise about point E to give polygon A'B'C'D' is B. BB′ = DD′.
When a polygon rotates counterclockwise, the corresponding sides remain equal in length. So, after the rotation, the length of side BB' will be equal to the length of side DD'.
The other options, A. A′E = AE and C. m∠ABC = m∠A'B'C', do not necessarily hold true after the rotation.